Fast photoresist model

Abstract

A method of modeling an image intended to reside in a photoresist film on a substrate is provided. A simulated latent acid image of the image is produced, the simulated latent acid image is compressed in a predetermined direction, and developed to a pattern that enables (a) transfer of the pattern to the substrate or (b) further modeling of the pattern for transfer to the substrate.

Description

RELATED APPLICATION/CLAIM OF PRIORITY

This application is related to and claims priority from provisional application Ser. No. 61/404,225, filed Sep. 29, 2010, which provisional application is incorporated by reference herein.

INTRODUCTION AND SUMMARY OF THE PRESENT INVENTION

The invention relates to a method of modeling an image intended to reside in a photoresist film on a substrate.

The method of the present invention includes electronically compressing a simulated latent acid image in a predetermined direction in the production of a pattern that can be used either for transferring the pattern to a substrate (via a mask or reticle), or for further modeling the pattern for transfer to the substrate.

In its basic aspect, the method of the present invention comprises electronically producing a simulated latent acid image of the image, compressing the simulated latent acid image in a predetermined direction, and developing the simulated latent acid image to a pattern that enables (a) transfer of the pattern to the substrate or (b) further modeling of the pattern for transfer to the substrate

In addition, the method preferably includes a sequence of steps where a development rate profile of the simulated latent acid image is produced, and then a final resist height is determined for the simulated latent acid image. Then, a critical dimension (CD) is determined from the final resist height, for the simulated latent acid image. Finally, a metrology offset is applied to the resist height, to complete development of the pattern. These aspects of the present invention are particularly useful where the image is a chemically amplified resist or an acid catalyzed resist, as will be apparent to those in the art.

In typical full resist models found in commercial software, the resist is electronically developed using small discreet time steps such that a development front is calculated in the x,y,z plane for each time step. This requires the computer to do extensive calculation and book keeping (thus requiring large amounts of CPU computational time and resources). The present invention produces the pattern by an electronic development rate profile that is not dependent on z, and thus significantly reduces the CPU computational time and resources to provide the modeling of the image.

Thus, a basic objective of the present invention is to create a modeling method that can operate faster than a full resist model but retains resist behavior development techniques such as quenching, post exposure bake, acid-base diffusion determination of inhibitor concentration.

Another basic object of the method of the present invention resides in compressing a simulated latent acid image in a predetermined direction (i.e. along the z direction or along the optical axis) in the production of the pattern.

Still another basic objective of the method of the present invention is to reduce computational time and resources to produce the pattern, while still replicating the results associated with a full photoresist model.

Further features of the present invention will be apparent from the following detailed description and the accompanying drawings and Exhibit.

BRIEF DESCRIPTION OF THE DRAWINGS AND EXHIBIT

FIG. 1 is a schematic illustration of the basic features of the method of the present invention;

FIGS. 2-11 show details of steps 1-10 of the method of FIG. 1;

FIGS. 12-19 show data from simulations that utilize the principles of the present invention; and

FIG. 20 schematically illustrates the characteristics of a photoresist pattern that can be produced by a modeling method according to the principles.

Exhibit A shows color images of FIGS. 1-20

DETAILED DESCRIPTION

As described above, the invention relates to a method of modeling an image intended to reside in a photoresist film on a substrate.

The method of modeling is preferably implemented on a general purpose computer and includes electronically compressing a simulated latent image in a predetermined direction in the production of a pattern that can be used either for transferring the pattern to a substrate, or for further modeling the pattern for transfer to the substrate. The method basically comprises electronically producing a simulated latent acid image of the image, compressing the simulated latent acid image in a predetermined direction, and developing the simulated latent acid image to a pattern that enables (a) transfer of the pattern to the substrate or (b) further modeling of the pattern for transfer to the substrate.

In a preferred version of the method of the present invention, the simulated latent acid image is electronically referenced to a set of x, y and z axes, and the predetermined direction comprises either of the z direction or along the optical axis related to imaging the substrate.

The method preferably includes an important sequence of steps where a development rate profile of the simulated latent acid image is produced, and then a final resist height is determined for the simulated latent acid image. Then, a critical dimension (CD) is determined from the final resist height, for the simulated latent acid image. Finally, a metrology offset is applied to the resist height, to complete development of the pattern. These aspects of the present invention are particularly useful where the image is a chemically amplified resist or an acid catalyzed resist, as will be apparent to those in the art.

In addition, a preferred embodiment of the method compressing the simulated latent image by electronically averaging the simulated latent acid image in the predetermined direction. The simulated latent acid image is electronically referenced to a set of x, y and z axes, or to an optical axis that is used in producing the image on the substrate, and the predetermined direction comprises the z direction or along the optical axis. Compressing the simulated latent image comprises electronically providing a weighted average for the simulated latent acid image along the z direction, where the bottom of the simulated latent image is weighted higher than the top part (which is close to the surface of the substrate).

FIG. 1 is an Overview of a computer implemented Simulation Procedure, according to the principles of the present invention. FIGS. 2-11 show details of steps 1-10 of the method of FIG. 1. By practicing the modeling method of the present invention, a pattern is produced that can be transferred to the substrate, or subjected to further modeling before being transferred to the substrate. As schematically illustrated in FIG. 20, in producing an image on a substrate (e.g. a semi conductor silicon wafer) a photoresist material (the “photoresist layer”) is applied to the substrate, and optically imaged (e.g. by a reticle or mask) to produce a pattern (referred to as a latent image) on the substrate. The imaged area is developed, in ways well known to those in the art, to produce the image on the substrate.

As shown by FIGS. 1 and 2, the first step in applicant's process of modeling an image intended to reside in a photoresist film on a substrate is to electronically determine (e.g. calculate) the image in a photoresist layer

• • For every focus, calculate the image in photoresist layer, using a simulator program
    • Focus=0 is defined at the top surface of the resist
  • All thin film properties should be included such as refractive index and extinction coefficient
    • n_resist, k_resist, Dill A≅0 for ArF
  • The image will be two dimensional (2D), described by the x-z axis, for a one dimensional (1D) feature, described by the x axis, such as a line or three dimensional (3D), described by the x-y-z axis, for a 2D feature, described by the x-y axis.

As shown by FIGS. 1 and 3, the next step in applicant's process is to electronically determine (calculate) the simulated latent acid image (the latent image that will be developed by acid treatment of the photoresist layer). In that calculation, applicant notes that

• • the image is electronically converted to a latent acid image by the following equation

Acid Image: I_A(x,y,z)=1−e^{−C·Dose·|IR(x,y,z)}

• • Where C is the Dill C parameter in units of cm2/mJ and Dose is the exposure dose in units of mJ/cm2
  • Applicant Notes that C*Dose=normalized exposure dose, where 1 is the
  • exposure equivalent to the resist clearing dose

As shown in FIGS. 1 and 4, the next step in applicant's process is to electronically compress the simulated latent acid image. In applicant's preferred process, this involves

• • electronically collapsing the simulated latent acid image from 2D/3D to 1D/2D
  • electronically using a weighted average as a function of depth in film, to compress the simulated latent acid image, by the equation below
    • weights are more linked to asymmetric properties of subsequent development steps
  • Still captures all the film properties including defocus, spherical aberration, standing wave effects, etc. . . .

${\stackrel{\_}{I}}_A\left(x,y\right)=\frac{\sum _{i=0}^dW_iI_A\left(x,y;z_i\right)}{\sum _{i=0}^dW_i},$

Weighted Average:

where W_i=1+γ_w(z_i−z_p)

• • zp=pivot depth and gw is the weighting slope: Nominal values of 0 for both but can be tuned
    • this is probably more important with thicker films
  • Note: applicant has used an initial linear weighting for simplicity. An exponential can be used as well, but we need to understand the functionality and effects of weighting the average image.
  • It should also be noted that in each of FIGS. 2-4, the axes (x, y and z) to which the photoresist model is referenced are illustrated (in FIGS. 2-4, the x and z axes are specifically shown, and the y axis would extend into and out of the x-z plane shown). In addition, it is noted that in FIGS. 2-4, the optical axis of the photoresist model coincides with the z axis. Still further, FIG. 4 also shows the bottom of the latent resist image weighted higher than the top part (which is close to the surface of the substrate).

As shown in FIGS. 1 and 5, the next step in applicant's process is to electronically model a quench of the simulated latent acid image with the initial base concentration, and electronically form the modified simulated latent acid image and quencher or base image concentrations

• • There is an initial base concentration in photoresist that will quench the simulated latent acid image. The approximation described herein assumes instantaneous quenching.
    • we end up with a modified acid concentration and a quencher or base “image” concentrations

Ī′_A(x,y)=Positive{Ī_A(x,y)−Q}, where Q=normalized quenching concentration and I′_A(x,y)≧0

Ī′_A(x,y)=Positive{Q−Ī_A(x,y)}, where Q=normalized quenching concentration and I′_Q(x,y)≧0

As shown in FIGS. 1 and 6, the next step in applicant's process is to electronically simulate diffusion by post exposure bake (PEB) of the simulated latent acid image using convolution

• • Assume that the acid and quencher images have separate diffusion lengths and possibly separate type of convolution kernels. Here, applicant has assumed Gaussian Kernels, but the literature also suggests double Gaussians or Lorentzian Kernels

Ī_A″(x,y)=β_A(Ī_A′(x,y)K_A(x,y)) and Ī_Q″(x,y)=(Ī_Q′(x,y)K_Q(x,y))

where β_A and β_Q are normalization constants to insure that ΣĪ_A′(x,y)=ΣĪ_A″(x,y) and ΣĪ_Q′(x,y)=ΣĪ_Q″(x,y)

$K_A\left(x,y\right)={}^{-\frac{x^2+y^2}{2{\sigma }_A^2}}\mathrm{and}K_Q\left(x,y\right)={\beta }_Q{}^{-\frac{x^2+y^2}{2{\sigma }_Q^2}},$

where the diffusion lengths are defined by σ_A and σ_Q

As shown by FIGS. 1 and 7, the next step in applicant's modeling process is electronic instantaneous quenching after PEB

• • Similar to the process step of FIG. 5, we get instantaneous quenching. We create a final simulated latent acid image profile for subsequent development that is soluble. We ignore the base as it is assumed not to be affected by developer

I_S(x,y)=Positive{Ī″_A(x,y)−Ī″_Q(x,y)}, where I_S(x,y)≧0

As shown in FIGS. 1 and 8, the next step in applicant's modeling process is to electronically create the inhibitor concentration

• • To work with existing development models, we need to transform the soluble simulated latent acid image into an inhibitor image. This is a function that describes the “insolubility” of the image, m. m=1 is unexposed resist and does not develop, while m=0 is totally exposed resist
  • This concentration occurs also during the PEB and has an amplification rate constant, k_a (sometimes called k_amp or k1)
    Inhibitor Concentration Image: m(x,y)=e^{−ka·tbake·IS(x,y)},
    where t_bake is the PEB bake time (usually 60 sec) and k_a is in units of sec⁻

As shown in FIGS. 1 and 9, the next step in applicant's modeling process is to electronically create a development rate profile of the simulated latent acid image

• • applicant uses a Mack development model to create the development rate, R(x,y) from the inhibitor concentration, m(x,y)

$R\left(x,y\right)=R_{\max }\frac{\left(a+1\right){\left(1-m\left(x,y\right)\right)}^n}{a+{\left(1-m\left(x,y\right)\right)}^n}+R_{\min },\mathrm{where}$ $a=\frac{\left(n+1\right)}{\left(n-1\right)}{\left(1-m_{\mathrm{th}}\right)}^n$

• • R_max and R_min are the maximum and minimum develop rates for fully exposed and unexposed resist. m_th is a threshold inhibitor concentration term. n is called the development contrast or sensitivity of the developer. The Rates are in units of nm/sec

As shown in FIGS. 1 and 10, the next step in applicant's modeling process is to electronically create a developed thickness profile of the simulated latent acid image

• • If we multiply our Rate, R(x,y), by the develop time, we get the nm of resist developed. Subtracting this from our initial undeveloped thickness gives the final resist height, H

H_dev=H_inital−t_devR(x,y), where t_dev is the develop time in sec

• • Note that we truncated the thickness at −10 nm.

As shown in FIGS. 1 and 11, the next step in applicant's process is to electronically determine (calculate) the linewidth or CD of the simulated latent acid image

• • We calculate the line width at some thickness value; hence,
    Line width at H(x,y)=h₀ given by the position of the right and left edges at a height of h₀ Hence if the edges are given as x_right(h₀)=x_r and x_left(h₀)=x_l,
    the line width or CD is given as: CD=abs(x_r−x_l)
  • Common sense tells us that h0=0 should be the threshold height; however, there are many issues with line width metrology, model accuracy, and calibration that we should let h0 be a calibratable parameter

As shown in FIG. 1, the final step in applicant's process is to electronically implement a metrology offset for the resist height.

• • There are often many issues comparing models from different simulators, experimental data measured with SEM, data measured with scatterometry.
  • Need to include one parameter called a “Metrology Offset” parameter, M₀
  • i.e.,

CD_final(x,y)=CD(x,y)−M₀

The modeling process described above produces (effectively transforms the simulated latent acid image into) a pattern (or stencil) that can be used in transferring an image to a photoresist layer, or which can be used as a development tool that can be further modeled by a developer to produce the pattern that cam be used in transferring an image to a photoresist layer.

It should be noted that the modeling sequence shown as steps 8-11 in FIGS. 1-11 is considered by applicant to be important in the modeling method of the present invention. That sequence is particularly useful where the image is a chemically amplified resist or an acid catalyzed resist, as will be apparent to those in the art.

Also, it should be noted that reshaping the simulated latent acid image by modeling techniques as shown in steps 4-7 (i.e. quenching the simulated latent acid image, post exposure bake, post exposure acid-base reaction, and/or creation of inhibitor concentration from the simulated latent acid image) retains latent image development techniques (quenching, post exposure bake, acid-base diffusion determination of inhibitor concentration) that are well known to those in the art. In this regard, it should be further noted that

• • a. After electronic conversion to acid the latent acid image is compressed by 1 dimension
  • b. If we assume instantaneous chemical reactions we can simplify the PEB (“Post Exposure Bake”) kinetics to a subtraction of quencher concentration profiles in combination with convolutions (known as a “Fukuda” approximation, which is a well known theory in the resist industry describing post exposure bake kinetics)
  • c. We can apply an electronic development model such as a “Mack” development tool (which is also well known in the resist industry) or any other development model to compute the inhibitor concentration
  • d. We can create an electronic developed thickness profile and apply a threshold to extract a linewidth.

In addition, it should be noted that The invention provides new features that are believed to be particularly useful in modeling an image intended to reside in a photoresist film on a substrate: For example,

• • a. Typical images in a photoresist film are either 2D (x transverse axis and z axial axis) or 3D (x,y,z). Subsequent modeling of the lithographic features consume a large amount of CPU and memory for such structures. The method of the present invention reduces the dimensionality of the problem by 1, after the image is converted to a latent acid image.
  • b. The method of the present invention reduces a large amount of CPU and memory that would otherwise be needed for modeling the image. The present invention reduces the dimensionality of the image, (by at least 1 dimension, after the image is converted to a latent acid image. Also, the method of the present invention adds the option of including a weighted average along the z direction. For example, the bottom of the latent resist image could be weighted higher than the top part (close to the surface of the substrate). This is necessary to counter balance any adverse effects of reducing the dimensionality of the image. The weighting is not limited to linear functions. For example it could be done with an exponential function.
  • c. In typical full resist models found in commercial software, the resist is electronically developed using small discreet time steps such that a development front is calculated in the x,y,z plane for each time step. This requires the computer to do extensive calculation and book keeping. The present invention produces the pattern by an electronic development rate profile that is not dependent on z; hence, the calculation time is almost instantaneous. Also, the use of the method described herein mitigates the adverse effects this approximation causes.
  • d. The method of the present invention effectively determines (calculates) photoresist line sizes (or x-y profiles) using a combination of an optical simulator to determine a pattern for the image, including a linewidth or CD (“Critical Dimension”) of a one-dimensional (1D) reticle (mask) feature or a two-dimensional (2D) reticle feature.
  • e. Also, compressing the simulated latent image comprises electronically averaging the simulated latent acid image in the predetermined direction. The simulated latent acid image is electronically referenced to a set of x, y and z axes, or to an optical axis that is used in producing the image on the substrate, and the predetermined direction comprises the z direction or along the optical axis. Compressing the simulated latent image comprises electronically providing a weighted average for the simulated latent acid image along the z direction, where the bottom of the simulated latent image is weighted higher than the top part (which is close to the surface of the substrate).

FIGS. 12-19 shown simulation data from a modeling process according to applicant's invention. Specifically,

FIG. 12 shows a FEM (“Focus Exposure Matrices”)_example

• • Note the slight asymmetry in focus, this should be there due to a finite resist thickness

Starting Values can be as shown in the table below

• • Applicant's approach is to try these values first
  • Keep the Rmin, Rmax, mth fixed for now
  • zp and Gw can be set to 0 unless we need them

Description	Symbol	Starting Values	Units
Image pivot depth	zp	0.00000	nm
Slope for Image weighting	Gw	0.01000	1/nm
Dill C	C	0.08130	cm2/mJ
Relative Quencher Conc.	Q	0.28740	au
Amplification constant	ka	0.08100	1/sec
Quencher Diffusion Length	Lq	3.33260	nm
Acid Diffusion Length	La	14.31180	nm
Development Contrast	n	10.90400	au
Inhibitor Threshold	mth	0.47700	au
Minimum Developmen Rate	Rmin	0.00100	nm/sec
Maximum Development Rate	Rmax	1538.00000	nm/sec
Metrology Threshold Height	h0	0.00000	nm
Focus Offset	f0	−0.04000	microns

Applicant's Calibration Method

• • a. Calibration can be done on any mix of data such as FEMs, CD through

Dose, CD through Pitch

• • b. Best and most robust calibration seems to be using multiple FEMs
  • you need to look at multiple exposure and focus levels to get proper calibration
  • the isofocal dose level (as a function of CD and pitch) is an extremely important parameter to calibrate. This is highly sensitive to resist chemistry.
  • c. KLA-Tencor has been successful in using 4 FEMs to get robust calibration using a full resist model
  • this may not work with approximate models, as it may only find local optimization
  • d. Probably need multiple 2-D structures, such as End-of-line, to calibrate approximate models
  • OPC models use 1500 structures with hundreds of 2D features
  • The “RoadRunner” model (described in Steps 1-11 above) designed to be more physical than OPC models.

FIG. 13 shows Applicant's Experimental FEM Data, Full_resist_FEMs for Calibration.xls

Applicant's Calibration Procedure

1. Rough calibration using dense line FEM, 50 nm Lines 100 nm Pitch

• • 1 focus at focus=best focus and CD to <30% CD to start
  • starting values
  • tune:
    • Dill's C, zp and Gw (and M0 if necessary)

2. Comprehensive tune with 1 FEMs

• • Tune: Dill's C, La, Q, Lq, ka,n
  • Fix: zp, Gw, mth, Rmax, Rmin, f0, M0

3. Comprehensive tune with 4 FEMs

• • all 4 FEMs
  • Restrict CD range to center of target

4. Comprehensive tune with 4 FEMs and End-of Line

• • Restrict EOL to focus=BF±25 nm and exposure=BE±3%

FIG. 14 shows applicant's simulation data for Quencher or Base

• • Fix focus at Best Focus and look at response through exposure Dose
    • 50 nm dense line (solid lines)
    • 70 nm isolated space (dashed lines)

FIG. 15 shows applicant's data for Acid Diffusion and Amplification

• • Fix focus at Best Focus and look at response through exposure Dose
    • 50 nm dense line (solid lines)
    • 70 nm isolated space (dashed lines)

FIG. 16 shows applicant's data for Development Contrast and mth

• • Fix focus at Best Focus and look at response through exposure Dose
    • 50 nm dense line (solid lines)
    • 70 nm isolated space (dashed lines)

FIG. 17 shows applicant's data for Development Rmax and Rmin

• • Fix focus at Best Focus and look at response through exposure Dose
    • 50 nm dense line (solid lines)
    • 70 nm isolated space (dashed lines)

FIG. 18 shows applicant's data for Weighted Average Parameters for latent image

• • Fix focus at Best Focus and look at response through exposure Dose
    • 50 nm dense line (solid lines)
    • 70 nm isolated space (dashed lines)

FIG. 19 shows applicant's data for Dill's C parameter: photospeed

• • Fix focus at Best Focus and look at response through exposure Dose
    • 50 nm dense line (solid lines)
    • 70 nm isolated space (dashed lines)

Thus, as seen from the foregoing detailed description, the present invention provides a method of modeling an image intended to reside in a photoresist film on a substrate, by producing a simulated latent acid image of the image, compressing the simulated latent acid image in a predetermined direction, and developed the compressed simulated latent acid image to a pattern that enables (a) transfer of the pattern to the substrate or (b) further modeling of the pattern for transfer to the substrate. With the foregoing disclosure in mind, those in the art will recognize various ways of modeling an image intended to reside in a photoresist film on a substrate, using the principles of the present invention.

Claims

1. A method of modeling an image intended to reside in a photoresist film on a substrate, comprising electronically producing a simulated latent acid image of the image, compressing the simulated latent acid image in a predetermined direction, and developing the simulated latent acid image to a pattern that enables transfer of the pattern to the substrate.

2. The method of claim 1, wherein compressing the simulated latent image comprises electronically averaging the simulated latent acid image in the predetermined direction.

3. The method of claim 1, wherein the simulated latent acid image is electronically referenced to a set of x, y and z axes, or to an optical axis that is used in producing the image on the substrate, and the predetermined direction comprises the z direction or along the optical axis.

4. The method of claim 3, wherein compressing the simulated latent image comprises electronically providing a weighted average for the simulated latent acid image along the predetermined direction.

5. The method of claim 4, wherein the bottom of the simulated latent image is weighted higher than the top part (which is close to the surface of the substrate).

6. The method of claim 1, further including creating a development rate profile of the simulated latent acid image.

7. The method of claim 6, further including creating a final resist height for the simulated latent acid image.

8. The method of claim 7, further including determining a critical dimension from the final resist height, for the simulated latent acid image.

9. The method of claim 8, further including applying a metrology offset to the resist height, to complete development of the pattern.

10. The method of claim 1, further comprising reshaping the simulated latent acid image by modeling techniques comprising (i) quenching the simulated latent acid image, (ii) post exposure bake, (iii) post exposure acid-base reaction, (iv) creation of inhibitor concentration from the simulated latent acid image, and (v) combinations of the foregoing.

11. A method of modeling an image intended to reside in a photoresist film on a substrate, comprising electronically producing a simulated latent acid image of the image, compressing the simulated latent acid image in a predetermined direction, and developing the simulated latent acid image to a pattern that enables further modeling of the pattern for transfer to the substrate.

12. The method of claim 11, wherein compressing the simulated latent image comprises electronically averaging the simulated latent acid image in the predetermined direction.

13. The method of claim 11, wherein the simulated latent acid image is electronically referenced to a set of x, y and z axes, or to an optical axis that is used in producing the image on the substrate, and the predetermined direction comprises the z direction or along the optical axis.

14. The method of claim 13, wherein compressing the simulated latent image comprises electronically providing a weighted average for the simulated latent acid image along the predetermined direction.

15. The method of claim 14, wherein the bottom of the simulated latent image is weighted higher than the top part (which is close to the surface of the substrate).

16. The method of claim 11, further including creating a development rate profile of the simulated latent acid image.

17. The method of claim 16, further including creating a final resist height for the simulated latent acid image.

18. The method of claim 17, further including determining a critical dimension from the final resist height, for the simulated latent acid image.

19. The method of claim 18, further including applying a metrology offset to the resist height, to complete development of the pattern.

20. The method of claim 11, further comprising reshaping the simulated latent acid image by modeling techniques comprising (i) quenching the simulated latent acid image, (ii) post exposure bake, (iii) post exposure acid-base reaction, (iv) creation of inhibitor concentration from the simulated latent acid image, and (v) combinations of the foregoing.